Steady heat transfer to water and viscoelastic fluid films facing down a vertical tube, for the case of uniform wad heat flux thermal boundary condition, was measured experimentally. The viscoelastic fluids studied were aqueous solutions of Praestol at 100, 204 and 500 ppm (by weight) concentration. The heat transfer to viscoelastic film was lower than the Newtonian prediction, at any given Prandtl number. A new correlation is proposed for dimensionless laminar and turbulent heat transfer coefficient in terms of the Weissenberg number, otter a range of 300 less than or equal to Re-a less than or equal to 6,500 and 6 less than or equal to Pr-a less than or equal to 30.